Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s. The Bell numbers are denoted , where is an integer greater than or equal to zero. Starting with , the first few Bell numbers are 1, 1, 2, 5, 15, 52, 203, 877, 4140, ... (sequence in the OEIS). The Bell number counts the number of different ways to partition a set that has exactly elements, or equivalently, the number of equivalence relations on it. also counts the number of different rhyme schemes for -line poems. As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, is the -th moment of a Poisson distribution with mean 1. (Wikipedia).
